1 Game Profile

1.1 Estimated Outcomes on BGG

This table displays the selected game’s current values on four BGG outcomes (UsersRated, Average, GeekRating, Weight) along with my predictive model(s) estimated values for where these games are likely to end up.

Published	ID	Name	Type	UserRatings	Average	GeekRating	Weight
2021	352963	Waterloo Solitaire	Current	52	7.58	5.55	1.50
			Estimated	200	7.64	5.71	1.77

To see more information about the game on boardgamegeek, click on the game’s ID or Name to go straight to the game’s profile page.

1.2 Game Description

Description
Waterloo Solitaire has 24 games. You take the role of Napoleon commanding the French army for 12 games against an opposing Allied autonomous player side, referred to as the Allied BOT side. And you take the role of Wellington for 12 games, commanding the Allied army against a French BOT side. Each opposing BOT side is rated for its skill; easy for 4 games, medium for 4 games, and hard for 4 games. One side is played by you (either Allied or French) and uses player actions for the side being playing. The BOT opponent uses the solitaire actions for the other side. A player can issue one action per game turn from their actions available for the side they are playing. He also has the option of using a Combined Arms Tactics with a supporting action to the one action played. Your choices can cause Die Roll Modifiers (DRM) that affects attacks with results that cause unit eliminations and tactical events to occur. The object of the game for the French player is to defeat the Allies by the end of the game. This is accomplished by removing all units in 2 of the 3 Allied infantry formations. The object for the Allied player is to avoid defeat by the end of the game. Both sides also have several other ways to win or lose before the game ends. You will need to provide a pen and one 6-sided die to play the game. -description from designer

1.3 Game Information

Information on the game’s designers, artists, families, mechanics and categories from BGG.

For the full profile of the selected game, click on the links in the table or go to https://boardgamegeek.com/boardgame/352963

1.4 Explaining Predictions

For each of the predictions above, I used models that were trained on historical boardgamegeek data in order to predict the selected game. How did the model(s) arrive at their predictions? The following plot displays Shapley values to indicate what features were most influential for the model’s predictions. Anything in blue increased the model’s predictions, anything in red decreased the model’s predictions.

2 Finding Similar Games

What games are similar to Waterloo Solitaire? I compare the selected game to every other game on boardgamegeek based on its mechanics, playing time, complexity, and game type. The tables below display the games which had the most similar data to Waterloo Solitaire. The reported similarity is the cosine similarity between the selected game and all other games published before 2021.

This similarity score ranges from -1 to 1, where similarity of 1 indicates that games are exactly identical (a game will have a score of 1 with itself).

Note: This analysis does not look at a game’s ratings on BGG, publisher, artist, or designer - it focuses on finding similar games based on how they play, not how they are rated or by their theme.

2.1 Most Similar Games

The table below displays games with the most similar data to Waterloo Solitaire. Click on a game’s ID or Name to go straight to its profile on boardgamegeek.

Rank	Published	ID	Name	Similarity	GeekRating	Average	Weight	UserRatings
--	2021	352963	Waterloo Solitaire	1.00	5.55	7.58	1.77	52
1	2008	28907	B-29 Superfortress	0.95	5.71	7.01	2.68	339
2	2007	30081	Salvo!	0.95	5.51	6.31	1.33	36
3	2011	85108	U-Boat Leader	0.94	5.71	7.01	2.53	348
4	1984	6929	Ranger	0.94	5.60	7.01	2.47	156
5	2000	12202	Battle of the Atlantic	0.94	5.52	6.60	1.88	38
6	2009	35350	Field Commander: Alexander	0.93	6.00	7.10	2.32	842
7	2006	23915	Solitaire Caesar	0.93	5.58	6.73	2.11	135
8	2013	147372	Irish Freedom	0.93	5.53	7.38	2.17	37
9	2018	227995	Raiders of the Deep: U-boats of the Great War, 1914-18	0.93	5.67	8.49	3.08	142
10	2016	126026	Gato Leader	0.93	5.58	7.10	2.67	101
11	1985	4413	Star Trek III	0.93	5.53	6.13	2.29	113
12	2013	136215	Red Menace	0.92	5.52	6.74	1.73	39
13	2010	65564	Hornet Leader: Carrier Air Operations	0.92	6.22	7.88	2.85	857
14	2020	189664	The Hunted: Twilight of the U-Boats, 1943-45	0.92	5.78	8.15	2.59	260
15	2014	163255	Reconquista	0.92	5.55	7.40	2.50	53
16	2019	294813	The Drifter	0.92	5.55	8.01	1.80	53
17	2016	190266	Sans Alliés	0.92	5.56	6.82	1.50	94
18	2014	57141	Codeword Cromwell: The German Invasion of England, 8 June 1940	0.91	5.68	8.01	3.00	135
19	2020	309721	Alone Against Fear	0.91	5.54	7.96		34
20	2016	197097	Four Against Darkness	0.91	6.15	7.53	2.09	1,261
21	2018	242589	NATO Air Commander	0.91	5.61	7.78	2.58	100
22	2020	255456	Beneath the Med: Regia Marina at Sea 1940-1943	0.91	5.66	8.13	2.47	146
23	1996	3807	Smokejumpers	0.91	5.56	6.60	2.33	93
24	2016	208800	Ceres: Operation Stolen Base	0.91	5.51	6.08	2.50	48
25	2016	206805	Agricola, Master of Britain	0.91	5.74	7.10	2.71	306

Click on the ID or Name for any game to go its profile page on boardgamegeek.

2.2 Most Similar, Highly Rated Games

What games are similar to Waterloo Solitaire while also being highly rated by the boardgamegeek community? In this table I multiply every neighboring game’s similarity score by its GeekRating. The resulting score is an attempt to balance these two quantities.

Rank	Published	ID	Name	Score	Similarity	GeekRating	Average	Weight	UserRatings
--	2021	352963	Waterloo Solitaire	5.55	1.00	5.55	7.58	1.77	52
1	2012	123955	Thunderbolt Apache Leader	5.85	0.90	6.50	8.04	3.22	1,222
2	2010	65564	Hornet Leader: Carrier Air Operations	5.74	0.92	6.22	7.88	2.85	857
3	2016	197097	Four Against Darkness	5.62	0.91	6.15	7.53	2.09	1,261
4	2009	35350	Field Commander: Alexander	5.59	0.93	6.00	7.10	2.32	842
5	2013	113873	The Hunters: German U-Boats at War, 1939-43	5.54	0.85	6.48	7.77	2.56	1,604
6	2011	42673	Field Commander: Napoleon	5.49	0.88	6.25	7.72	2.80	970
7	2008	22877	Fields of Fire	5.45	0.86	6.37	7.85	4.23	1,194
8	2013	134520	Phantom Leader Deluxe	5.42	0.90	6.00	8.06	2.65	490
9	2008	28907	B-29 Superfortress	5.42	0.95	5.71	7.01	2.68	339
10	2011	85108	U-Boat Leader	5.37	0.94	5.71	7.01	2.53	348
11	2019	196257	Castle Itter	5.32	0.90	5.90	7.79	2.31	413
12	2020	189664	The Hunted: Twilight of the U-Boats, 1943-45	5.31	0.92	5.78	8.15	2.59	260
13	2008	28829	Field Commander: Rommel	5.31	0.88	6.02	7.00	2.46	1,004
14	2009	35614	Where There Is Discord: War in the South Atlantic	5.29	0.89	5.93	7.91	3.11	411
15	2017	160903	Target for Today	5.26	0.90	5.86	8.07	3.40	393
16	2018	155122	1066, Tears to Many Mothers	5.26	0.89	5.92	7.10	2.26	702
17	2010	41490	Phantom Leader	5.25	0.89	5.90	7.46	2.60	485
18	2018	227995	Raiders of the Deep: U-boats of the Great War, 1914-18	5.25	0.93	5.67	8.49	3.08	142
19	1984	6929	Ranger	5.24	0.94	5.60	7.01	2.47	156
20	2007	30081	Salvo!	5.22	0.95	5.51	6.31	1.33	36
21	2013	144568	Dawn of the Zeds (Second edition)	5.22	0.85	6.12	7.86	3.17	648
22	2016	206805	Agricola, Master of Britain	5.20	0.91	5.74	7.10	2.71	306
23	2014	57141	Codeword Cromwell: The German Invasion of England, 8 June 1940	5.19	0.91	5.68	8.01	3.00	135
24	2006	23915	Solitaire Caesar	5.18	0.93	5.58	6.73	2.11	135
25	2016	126026	Gato Leader	5.17	0.93	5.58	7.10	2.67	101

2.3 Why Are Games Considered Similar?

I first ran a dimension reduction method (PCA) to identify the main points of variation for games on BGG. The first 25 components explained roughly 50% of the overall variation in the dataset, so I computed the cosine similarity between every game’s score on these 25 components.

2.3.1 Plotting All Games

The following plot shows every game on BGG plotted on the first two principal components of variation. I then highlight where the selected game and its nearest neighbors fall on these first two components.

2.3.2 Game Profiles

Similarity scores are based on 25 principal components - the next table displays the selected game and its neighbors profiles on each of these components.

2.3.3 Examining Components

What are these components? The following plot shows which features contribute the most to each component.

Published	ID	Name	Publisher(s)	Designer(s)	Artist(s)	Categories	Families	Mechanics
2021	352963	Waterloo Solitaire	Worthington Publishing, LLC	Sean Cooke	Sean Cooke	Book	Country: Belgium	Dice Rolling
				Mike Wylie	Denis Dighton	Napoleonic	Country: France	Paper-and-Pencil
				Grant Wylie		Wargame	History: Napoleonic Wars	Solo / Solitaire Game
							Players: Solitaire Only Games
							Players: Solitaire Only Wargames
							Players: Wargames with Solitaire Rules
							Series: Worthington Original Bookgames

Individual Game Analysis